The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  1  2  0  1 12  8  2  1  2  1  2  4  2 12  1  1  1  2  1  2  2  1  1  1  2  1  1  2  4  1  2  1  1
 0  2  0  0  0  2 14  2  4 12 14 10 12 14 12 14  4 14  0  4  2  6 12  8 14  4 14  8  4  0 10 10  2 12  4  2  8 14  6  6  2  2 12 12  6  4  4 14 12  6  0  4  8  2 14  6  2  2  2  8  8 14  8
 0  0  2  0  2  2 10  8  0  0  2 10  6  4 14  4  8  8  4  2 14  6 14  4 12 14  0  0  2  2  2  6 12  4  2 10  0  0 12 10  2 14 14  2 14 12  4 12 10  2  6 14  2  4  8 12 12  0  0  4  2  4 10
 0  0  0  2  2  8  2  6 14  4  4 14 14 10 12  4 10 14 12  6 12 10  4 12  8  2 14 10  4 14 14  8  2 14  6  6 14  4  0  8  8  0  8 10  8  2  0 12  8  0 14  6  4  8  6  6 12  4  4  0  0  2  0
 0  0  0  0  4  0  4 12 12 12 12  8  8  0 12 12 12  0  0  4  0  8  8 12  8  0  4  4  0  4 12  0  8  8 12  4  8  4 12  8 12  8  4  8  8  4 12  8  4  8  8  4  8  8  8  8  8  8 12  4  4  0 12

generates a code of length 63 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+216x^55+418x^56+778x^57+1247x^58+1810x^59+2507x^60+3114x^61+4082x^62+4464x^63+4134x^64+3524x^65+2403x^66+1520x^67+1025x^68+606x^69+430x^70+250x^71+99x^72+70x^73+26x^74+26x^75+8x^76+4x^77+3x^78+2x^79+1x^86

The gray image is a code over GF(2) with n=504, k=15 and d=220.
This code was found by Heurico 1.16 in 18.2 seconds.